Generating genus‐<i>n</i>‐to‐<i>m</i>mesh morphing using spherical parameterization

Abstract

Abstract Surface parameterization is a fundamental tool in computer graphics and benefits many applications such as texture mapping, morphing, and re‐meshing. Many spherical parameterization schemes with very nice properties have been proposed and widely used in the past. However, it is well known that the spherical parameterization is limited to genus‐ 0 models. In this paper, we first propose a novel framework to extend spherical parameterization for handling a genus‐n surface. In this framework, we represent a surface S of arbitrary genus by a positive mesh O and several negative meshes N i . Each negative surface is used to represent a hole. A positive surface O is obtained by removing all holes in the original surface S. Then, both positive and negative meshes are genus‐0 and can be spherically parameterized, respectively. To compute S, we can use a Boolean difference operation to subtract negative N i from a positive O. Next, we apply this novel framework to generate genus‐n‐to‐m mesh morphing application without restriction of n = m. Finally, there are many interesting non‐genus‐0 mesh morphing sequences generated. Copyright © 2006 John Wiley &amp; Sons, Ltd.